Abstract: Aiming at the problem that the traditional matrix-completion unconstrained optimization model had poor robustness in dealing with missing matrices damaged by singular noise, we proposed an adaptive robust matrix completion method. In this method, truncated kernel norm was used as the low-rank approximation of the rank function in the objective function, and the F-norm robust to singular noise was used as the loss term to recover the missing values in the matrix, so as to reduce the influence of outliers on the algorithm and improve the recovery accuracy. In the process of solving this model, a dynamic weight parameter was introduced by using convex optimization technique, which could be used to adjust the next update adaptively according to the current recovery error when updating the recovery value, and then an effective iteration method was established to solve the optimization problem. The experimental results show that the algorithm has better robustness and accuracy when dealing with matrices damaged by singular noise, so that better image restoration effects can be obtained.

Key words: matrix completion, truncated kernel norm, singular noise, square F-norm